### Home > A2C > Chapter 4 > Lesson 4.3.1 > Problem4-140

4-140.

Sketch the graph of $y = 2\left(x − 1\right)^{2} + 4$.

1. Now rewrite the equation $y = 2\left(x − 1\right)^{2} + 4$ without parentheses. Remember the order of operations!

• $y = 2x^{2} − 4x + 6$

1. What would the difference be between the graphs of the two equations above? This is sort of a trick question, but explain your reasoning.

Where is the vertex of $y = 2\left(x − 1\right)^{2} + 4$? Or $y = 2x^{2} − 4x +$?
What are their stretch factors?

2. What is the parent of $y = 2\left(x − 1\right)^{2} + 4$?

Refer to the Math Notes box from Lesson 4.3.2.

3. What is the parent of $y = 2x^{2 }− 4x + 6$?

See part (c).